From 273b2246a20b01fbb693c7b16631255804d28b2b Mon Sep 17 00:00:00 2001 From: Anders Andreasen <58475535+andr1976@users.noreply.github.com> Date: Tue, 30 Dec 2025 14:27:12 +0100 Subject: [PATCH 1/6] Adding peak heat loads --- src/hyddown/fire.py | 45 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 45 insertions(+) diff --git a/src/hyddown/fire.py b/src/hyddown/fire.py index 3fc11b0..b0ad4ac 100644 --- a/src/hyddown/fire.py +++ b/src/hyddown/fire.py @@ -69,6 +69,45 @@ def jet_fire_scandpower(Tvessel): return stefan_boltzmann(alpha, e_flame, e_surface, h, Tflame, Tradiative, Tvessel) +def jet_fire_peak_large_scandpower(Tvessel): + """ + Incident heat flux of 350 kW/m2 + """ + alpha = 0.85 + e_flame = 1 + e_surface = 0.85 + h = 100 + Tflame = 1429.61 + Tradiative = 1429.61 + return stefan_boltzmann(alpha, e_flame, e_surface, h, Tflame, Tradiative, Tvessel) + + +def jet_fire_peak_small_scandpower(Tvessel): + """ + Incident heat flux of 250 kW/m2 + """ + alpha = 0.85 + e_flame = 1 + e_surface = 0.85 + h = 100 + Tflame = 1279.29 + Tradiative = 1279.29 + return stefan_boltzmann(alpha, e_flame, e_surface, h, Tflame, Tradiative, Tvessel) + + +def pool_fire_peak_scandpower(Tvessel): + """ + Incident heat flux of 150 kW/m2 + """ + alpha = 0.85 + e_flame = 1 + e_surface = 0.85 + h = 30 + Tflame = 1212.54 + Tradiative = 1212.54 + return stefan_boltzmann(alpha, e_flame, e_surface, h, Tflame, Tradiative, Tvessel) + + def sb_fire(T_vessel, fire_type): if fire_type == "api_jet": Q = jet_fire_api521(T_vessel) @@ -78,6 +117,12 @@ def sb_fire(T_vessel, fire_type): Q = pool_fire_scandpower(T_vessel) elif fire_type == "scandpower_jet": Q = jet_fire_scandpower(T_vessel) + elif fire_type == "scandpower_jet_peak_large": + Q = jet_fire_peak_large_scandpower(T_vessel) + elif fire_type == "scandpower_jet_peak_small": + Q = jet_fire_peak_small_scandpower(T_vessel) + elif fire_type == "scandpower_pool_peak": + Q = pool_fire_peak_scandpower(T_vessel) else: raise ValueError("Unknown Stefan-Bolzmann fire heat load") return Q From 4c76617a2aa54144224c76f878452c73cdc4a392 Mon Sep 17 00:00:00 2001 From: Anders Andreasen <58475535+andr1976@users.noreply.github.com> Date: Tue, 30 Dec 2025 14:36:36 +0100 Subject: [PATCH 2/6] Rupture calc WIP --- src/hyddown/hdclass.py | 120 +++++++++++++++++++++++++++++++++++------ 1 file changed, 104 insertions(+), 16 deletions(-) diff --git a/src/hyddown/hdclass.py b/src/hyddown/hdclass.py index 048f800..0851152 100644 --- a/src/hyddown/hdclass.py +++ b/src/hyddown/hdclass.py @@ -1042,27 +1042,15 @@ def run(self, disable_pbar=True): self.Q_outer[i] = ( fire.sb_fire(self.T_vessel[i - 1], self.fire_type) - # ( - # self.sb_heat_load(self.time_array[i]) - # - 0.85 * 5.67e-8 * self.T_vessel[i - 1] ** 4 - # ) * (self.surf_area_inner - wetted_area) * self.surf_area_outer / self.surf_area_inner ) self.q_outer[i] = fire.sb_fire(self.T_vessel[i - 1], self.fire_type) - # ( - # self.sb_heat_load(self.time_array[i]) - # - 0.85 * 5.67e-8 * self.T_vessel[i - 1] ** 4 - # ) self.Q_outer_wetted[i] = ( fire.sb_fire(self.T_vessel_wetted[i - 1], self.fire_type) - # ( - # self.sb_heat_load(self.time_array[i]) - # - 0.85 * 5.67e-8 * self.T_vessel_wetted[i - 1] ** 4 - # ) * wetted_area * self.surf_area_outer / self.surf_area_inner @@ -1070,10 +1058,6 @@ def run(self, disable_pbar=True): self.q_outer_wetted[i] = fire.sb_fire( self.T_vessel_wetted[i - 1], self.fire_type ) - # ( - # self.sb_heat_load(self.time_array[i]) - # - 0.85 * 5.67e-8 * self.T_vessel_wetted[i - 1] ** 4 - # ) if np.isnan(self.Q_outer_wetted[i]): self.Q_outer_wetted[i] = 0 @@ -1701,6 +1685,110 @@ def plot_tprofile(self, filename=None, verbose=True): if verbose: plt.show() + def analyze_rupture(self, filename=None): + from hyddown.materials import steel_Cp, ATS, von_mises + from hyddown import fire + + pres = lambda x: np.interp(x, self.time_array, self.P) + q_unwetted = lambda x: np.interp(x, self.time_array, self.q_inner) + q_wetted = lambda x: np.interp(x, self.time_array, self.q_inner_wetted) + + T0_unwetted = self.T_vessel[0] + T0_wetted = self.T_vessel_wetted[0] + + thk = self.thickness + rho = self.vessel_density + inner_diameter = self.diameter + + dt = 10 + max_time = self.time_array[-1] + tsteps = int(max_time / dt) + + T_wetted_wall = np.zeros(tsteps + 1) + T_unwetted_wall = np.zeros(tsteps + 1) + T_wetted_wall[0] = T0_wetted + T_unwetted_wall[0] = T0_unwetted + peak_times = np.zeros(tsteps + 1) + peak_times[0] = 0 + + for i in range(tsteps): + peak_times[i + 1] = peak_times[i] + dt + q_fire_wetted = fire.sb_fire(T_wetted_wall[i], self.sb_peak_fire_type) + q_fire_unwetted = fire.sb_fire(T_unwetted_wall[i], self.sb_peak_fire_type) + T_wetted_wall[i + 1] = T_wetted_wall[i] + ( + q_fire_wetted - q_wetted(peak_times[i]) + ) * dt / (thk * rho * steel_Cp(T_wetted_wall[i], self.material)) + T_unwetted_wall[i + 1] = T_unwetted_wall[i] + ( + q_fire_unwetted - q_unwetted(peak_times[i]) + ) * dt / (thk * rho * steel_Cp(T_unwetted_wall[i], self.material)) + + ATS_wetted = np.array([ATS(T, self.material) for T in T_wetted_wall]) + ATS_unwetted = np.array([ATS(T, self.material) for T in T_unwetted_wall]) + von_mises_wetted = von_mises_unwetted = np.array( + [von_mises(pres(time), inner_diameter, thk) for time in peak_times] + ) + + self.peak_times = peak_times + self.von_mises = von_mises_unwetted + self.ATS_unwetted = ATS_unwetted + self.ATS_wetted = ATS_wetted + self.peak_T_wetted = T_wetted_wall + self.peak_T_unwetted = T_unwetted_wall + + if np.all(ATS_unwetted > von_mises_unwetted) == True: + self.rupture_time = None + # print("No rupture") + elif np.all(ATS_unwetted < von_mises_unwetted) == True: + self.rupture_time = 0 + # print("Rupture at time=0") + else: + rupture_idx = np.where(ATS_unwetted < von_mises_unwetted)[0][0] + self.rupture_time = ( + peak_times[rupture_idx - 1] + peak_times[rupture_idx] + ) / 2 + # print("Rupture time +/- 5 s:", self.rupture_time) + # print("Rupture pressure (bar)", pres(peak_times[rupture_idx - 1])) + + from matplotlib import pyplot as plt + + plt.figure(1) + plt.plot(peak_times, von_mises_wetted / 1e6, label="von Mises stress") + + plt.plot(peak_times, ATS_unwetted / 1e6, label="ATS unwetted wall") + if sum(self.liquid_dyn_level) > 0: + plt.plot(peak_times, ATS_wetted / 1e6, label="ATS wetted wall") + plt.xlabel("Time (s)") + plt.ylabel("Allowable Tensile Strength / von Mises Stress (MPa)") + plt.legend(loc="best") + if filename is not None: + plt.savefig( + filename + "_ATS_vonmises.png", + ) + plt.figure(2) + if sum(self.liquid_dyn_level) > 0: + plt.plot(peak_times, T_wetted_wall - 273.15, label="T wetted wall") + plt.plot(peak_times, T_unwetted_wall - 273.15, label="T unwetted wall") + plt.xlabel("Time (s)") + plt.ylabel("Wall temperature (C)") + plt.legend(loc="best") + if filename is not None: + plt.savefig( + filename + "_peak_wall_temp.png", + ) + + plt.figure(3) + plt.plot( + peak_times, + np.array([pres(time) for time in peak_times]) / 1e5, + label="Pressure", + ) + plt.xlabel("Time (s)") + plt.ylabel("Pressure (bar)") + plt.legend(loc="best") + + if filename is None: + plt.show() + def __str__(self): return "HydDown vessel filling/depressurization class" From f676c44f1a382949caa7a221622471e62b1a3680 Mon Sep 17 00:00:00 2001 From: Anders Andreasen <58475535+andr1976@users.noreply.github.com> Date: Tue, 30 Dec 2025 15:21:03 +0100 Subject: [PATCH 3/6] Rupture WIP --- .../__pycache__/materials.cpython-311.pyc | Bin 8752 -> 8752 bytes src/hyddown/examples/rupture.yml | 35 ++++++++++++++++++ src/hyddown/fire.py | 2 +- src/hyddown/hdclass.py | 25 +++++++++---- src/hyddown/validator.py | 22 +++++++++++ 5 files changed, 75 insertions(+), 9 deletions(-) create mode 100644 src/hyddown/examples/rupture.yml diff --git a/src/hyddown/__pycache__/materials.cpython-311.pyc b/src/hyddown/__pycache__/materials.cpython-311.pyc index 8c2ae1425a8cfad49a95150e85a072a7f4113c47..0eb687d55e710884419ea5c81375e8931e246fbf 100644 GIT binary patch delta 20 acmdnsvcZLWIWI340}!0J6ugmJRS5t;Xa%nT delta 20 acmdnsvcZLWIWI340}vReN^j&=RRRDvuLN}f diff --git a/src/hyddown/examples/rupture.yml b/src/hyddown/examples/rupture.yml new file mode 100644 index 0000000..b48a06c --- /dev/null +++ b/src/hyddown/examples/rupture.yml @@ -0,0 +1,35 @@ +vessel: + length: 9 + diameter: 3 + orientation: "vertical" + type: "Flat-end" + heat_capacity: 500 + density: 7700 + thickness: 0.136 +initial: + temperature: 298.15 + pressure: 11500000 + fluid: "CH4" +calculation: + type: "energybalance" + time_step: 1 + end_time: 3000. +valve: + flow: "discharge" + type: "psv" + diameter: 0.013 + discharge_coef: 0.975 + set_pressure: 13500000 + blowdown: 0.1 + back_pressure: 101300. +#valve: +# flow: "discharge" +# type: "relief" +# set_pressure: 13500000 +# back_pressure: 101300. +heat_transfer: + type: "s-b" + fire: "scandpower_pool" +rupture: + material: "CS_360LT" + fire: "scandpower_jet_peak_large" \ No newline at end of file diff --git a/src/hyddown/fire.py b/src/hyddown/fire.py index b0ad4ac..7978cfd 100644 --- a/src/hyddown/fire.py +++ b/src/hyddown/fire.py @@ -117,7 +117,7 @@ def sb_fire(T_vessel, fire_type): Q = pool_fire_scandpower(T_vessel) elif fire_type == "scandpower_jet": Q = jet_fire_scandpower(T_vessel) - elif fire_type == "scandpower_jet_peak_large": + elif fire_type == "scandpower_jet_peak_large": Q = jet_fire_peak_large_scandpower(T_vessel) elif fire_type == "scandpower_jet_peak_small": Q = jet_fire_peak_small_scandpower(T_vessel) diff --git a/src/hyddown/hdclass.py b/src/hyddown/hdclass.py index 0851152..ee5d282 100644 --- a/src/hyddown/hdclass.py +++ b/src/hyddown/hdclass.py @@ -191,6 +191,13 @@ def read_input(self): # - functional mass flow self.thickness = 0 + if "rupture" in self.input: + self.rupture_material = self.input["rupture"]["material"] + if "fire" in self.input["rupture"]: + self.rupture_fire = self.input["rupture"]["fire"] + else: + self.rupture_fire = "api_jet" + # Reading heat transfer related data/information if "heat_transfer" in self.input: self.heat_method = self.input["heat_transfer"]["type"] @@ -1713,17 +1720,19 @@ def analyze_rupture(self, filename=None): for i in range(tsteps): peak_times[i + 1] = peak_times[i] + dt - q_fire_wetted = fire.sb_fire(T_wetted_wall[i], self.sb_peak_fire_type) - q_fire_unwetted = fire.sb_fire(T_unwetted_wall[i], self.sb_peak_fire_type) + q_fire_wetted = fire.sb_fire(T_wetted_wall[i], self.rupture_fire) + q_fire_unwetted = fire.sb_fire(T_unwetted_wall[i], self.rupture_fire) T_wetted_wall[i + 1] = T_wetted_wall[i] + ( q_fire_wetted - q_wetted(peak_times[i]) - ) * dt / (thk * rho * steel_Cp(T_wetted_wall[i], self.material)) + ) * dt / (thk * rho * steel_Cp(T_wetted_wall[i], self.rupture_material)) T_unwetted_wall[i + 1] = T_unwetted_wall[i] + ( q_fire_unwetted - q_unwetted(peak_times[i]) - ) * dt / (thk * rho * steel_Cp(T_unwetted_wall[i], self.material)) + ) * dt / (thk * rho * steel_Cp(T_unwetted_wall[i], self.rupture_material)) - ATS_wetted = np.array([ATS(T, self.material) for T in T_wetted_wall]) - ATS_unwetted = np.array([ATS(T, self.material) for T in T_unwetted_wall]) + ATS_wetted = np.array([ATS(T, self.rupture_material) for T in T_wetted_wall]) + ATS_unwetted = np.array( + [ATS(T, self.rupture_material) for T in T_unwetted_wall] + ) von_mises_wetted = von_mises_unwetted = np.array( [von_mises(pres(time), inner_diameter, thk) for time in peak_times] ) @@ -1755,7 +1764,7 @@ def analyze_rupture(self, filename=None): plt.plot(peak_times, von_mises_wetted / 1e6, label="von Mises stress") plt.plot(peak_times, ATS_unwetted / 1e6, label="ATS unwetted wall") - if sum(self.liquid_dyn_level) > 0: + if self.liquid_level.all() != 0: plt.plot(peak_times, ATS_wetted / 1e6, label="ATS wetted wall") plt.xlabel("Time (s)") plt.ylabel("Allowable Tensile Strength / von Mises Stress (MPa)") @@ -1765,7 +1774,7 @@ def analyze_rupture(self, filename=None): filename + "_ATS_vonmises.png", ) plt.figure(2) - if sum(self.liquid_dyn_level) > 0: + if self.liquid_level.all() != 0: plt.plot(peak_times, T_wetted_wall - 273.15, label="T wetted wall") plt.plot(peak_times, T_unwetted_wall - 273.15, label="T unwetted wall") plt.xlabel("Time (s)") diff --git a/src/hyddown/validator.py b/src/hyddown/validator.py index 308b4a1..de294a3 100644 --- a/src/hyddown/validator.py +++ b/src/hyddown/validator.py @@ -91,6 +91,19 @@ def validate_mandatory_ruleset(input): }, }, }, + "rupture": { + "required": False, + "type": "dict", + "allow_unknown": False, + "schema": { + "material": { + "required": True, + "type": "string", + "allowed": ["CS_235LT", "CS_360LT", "SS316", "Duplex", "6Mo"], + }, + "fire": {"required": False, "type": "string"}, + }, + }, "valve": { "required": True, "type": "dict", @@ -369,6 +382,7 @@ def heat_transfer_validation(input): "initial": {"required": True}, "calculation": {"required": True}, "validation": {"required": False}, + "rupyture": {"required": False}, "valve": {"required": True}, "vessel": { "required": True, @@ -448,6 +462,7 @@ def heat_transfer_validation(input): "initial": {"required": True}, "calculation": {"required": True}, "validation": {"required": False}, + "rupture": {"required": False}, "valve": {"required": True}, "vessel": { "required": True, @@ -498,6 +513,7 @@ def heat_transfer_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "valve": {"required": True}, + "rupture": {"required": False}, "vessel": { "required": True, "type": "dict", @@ -548,6 +564,7 @@ def heat_transfer_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "valve": {"required": True}, + "rupture": {"required": False}, "vessel": { "required": True, "type": "dict", @@ -627,6 +644,7 @@ def valve_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "vessel": {"required": True}, + "rupture": {"required": False}, "heat_transfer": {"required": True}, "valve": { "required": True, @@ -661,6 +679,7 @@ def valve_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "vessel": {"required": True}, + "rupture": {"required": False}, "heat_transfer": {"required": False}, "valve": { "required": True, @@ -695,6 +714,7 @@ def valve_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "vessel": {"required": True}, + "rupture": {"required": False}, "heat_transfer": {"required": False}, "valve": { "required": True, @@ -726,6 +746,7 @@ def valve_validation(input): schema_control_valve = { "initial": {"required": True}, + "rupture": {"required": False}, "calculation": {"required": True}, "validation": {"required": False}, "vessel": {"required": True}, @@ -761,6 +782,7 @@ def valve_validation(input): "calculation": {"required": True}, "validation": {"required": False}, "vessel": {"required": True}, + "rupture": {"required": False}, "heat_transfer": {"required": False}, "valve": { "required": True, From 36242e12499efa1c1daa1e078686f272595243cc Mon Sep 17 00:00:00 2001 From: Anders Andreasen <58475535+andr1976@users.noreply.github.com> Date: Tue, 30 Dec 2025 17:02:10 +0100 Subject: [PATCH 4/6] Adding test for S-B fire heat load --- src/hyddown/examples/rupture.yml | 12 +- src/hyddown/test_all.py | 84 +- validation/rupture_history.csv | 1802 ++++++++++++++++++++++++++++++ 3 files changed, 1887 insertions(+), 11 deletions(-) create mode 100644 validation/rupture_history.csv diff --git a/src/hyddown/examples/rupture.yml b/src/hyddown/examples/rupture.yml index b48a06c..c7c1b94 100644 --- a/src/hyddown/examples/rupture.yml +++ b/src/hyddown/examples/rupture.yml @@ -13,20 +13,12 @@ initial: calculation: type: "energybalance" time_step: 1 - end_time: 3000. + end_time: 900. valve: flow: "discharge" - type: "psv" - diameter: 0.013 - discharge_coef: 0.975 + type: "relief" set_pressure: 13500000 - blowdown: 0.1 back_pressure: 101300. -#valve: -# flow: "discharge" -# type: "relief" -# set_pressure: 13500000 -# back_pressure: 101300. heat_transfer: type: "s-b" fire: "scandpower_pool" diff --git a/src/hyddown/test_all.py b/src/hyddown/test_all.py index e57f8b0..4bf2283 100644 --- a/src/hyddown/test_all.py +++ b/src/hyddown/test_all.py @@ -339,6 +339,88 @@ def test_sim_stefan_boltzmann(): hdown.run() +def test_sim_rupture(): + import os + import pandas as pd + import matplotlib.pyplot as plt + from hyddown import HydDown + import scienceplots + + plt.style.use(["science", "nature"]) + + input = get_example_input("rupture.yml") + hdown = HydDown(input) + hdown.run() + + fname = os.path.join( + os.path.abspath(os.path.dirname(__file__)), + "..", + "..", + "validation", + "rupture_history.csv", + ) + df_ref = pd.read_csv(fname) + plt.figure(1) + plt.plot(hdown.time_array, hdown.P, label="Hyddown", linestyle="-", color="#125A56") + plt.plot( + df_ref["Time"], + df_ref["Vapour - Pressure"] * 1e5 + 1.013e5, + label="Unisim", + linestyle="--", + color="#125A56", + ) + plt.xlabel("Time (s)") + plt.ylabel("Pressure (Pa)") + plt.legend() + + plt.figure(2) + plt.plot( + hdown.time_array, + hdown.T_fluid - 273.15, + label="Hyddown - Gas", + linestyle="-", + color="#FF6F61", + ) + plt.plot( + df_ref["Time"], + df_ref["Vapour - Temperature"], + label="Unisim - Gas", + linestyle="--", + color="#FF6F61", + ) + plt.plot( + hdown.time_array, + hdown.T_vessel - 273.15, + label="Hyddown - Wall", + linestyle="-", + color="#00767B", + ) + plt.plot( + df_ref["Time"], + df_ref[ + "Vessel - Heat Loss: Inner Wall Temperatures (Heat Loss: Inner Wall Temperatures_1)" + ], + label="Unisim - Wall", + linestyle="--", + color="#00767B", + ) + plt.xlabel("Time (s)") + plt.ylabel("Temperature (°C)") + plt.legend() + # plt.show() + + assert hdown.T_vessel[-1] == pytest.approx( + df_ref[ + "Vessel - Heat Loss: Inner Wall Temperatures (Heat Loss: Inner Wall Temperatures_1)" + ][-1:] + + 273.15, + abs=10, + ) + assert hdown.T_fluid[-1] == pytest.approx( + df_ref["Vapour - Temperature"][-1:] + 273.15, rel=0.01 + ) + + def test_dataframe(): from hyddown import HydDown @@ -540,4 +622,4 @@ def test_boiling_heat_transfer(): if __name__ == "__main__": - test_mdot_filling() + test_sim_rupture() diff --git a/validation/rupture_history.csv b/validation/rupture_history.csv new file mode 100644 index 0000000..a826086 --- /dev/null +++ b/validation/rupture_history.csv @@ -0,0 +1,1802 @@ +Time,Vapour - Temperature,Vapour - Pressure,Vapour - Mass Flow,VapourOut - Comp Mole Frac (Methane),VapourOut - Temperature,VapourOut - Mass Flow,Liquid - Pressure,Liquid - Mass Flow,LiquidOut - Temperature,LiquidOut - Mass Flow,LiquidOut - Comp Mole Frac (Methane),Vessel - Bulk Vapour Temperature,Vessel - Bulk Liquid Temperature,Vessel - Heat Loss: Inner Wall Temperatures (Heat Loss: Inner Wall Temperatures_1),Vessel - Heat Loss: Inner Wall Temperatures (Heat Loss: Inner Wall Temperatures_2),Vessel - Heat Loss: Inner Wall Temperatures (Heat Loss: Inner Wall Temperatures_3),Vessel - Vapour Mass,Vessel - Liquid Mass,Vessel - Heat Loss: Inside Vap Phase Heat Loss U,Vessel - Heat Loss: Outside Heat Loss U,Vessel - Heat Loss: Inside Liq Phase Heat Loss U,Vessel - Heat Loss: Vapour To Liquid Heat Loss U,Vessel - Heat Loss: Overall Heat Loss,Vessel - HX Duty: Heat Flow +0.5,25.0919,114,0,1,-31.4356,0,114,0,-31.4356,0,1,25.0919,25.0919,36.5165,36.5165,36.5165,5791.19,0,538.698,10.4569,729.76,3.01E-103,333.672,0 +1,25.1288,114,0,1,-31.4356,0,114,0,-31.4356,0,1,25.1288,25.1288,36.5201,36.5201,36.5201,5791.19,0,429.178,11.1982,581.57,3.01E-103,134.322,0 +1.5,25.1355,114.002,0,1,-31.4356,0,114.002,0,-31.4356,0,1,25.1355,25.1355,36.5201,36.5201,36.5201,5791.19,0,429.178,11.1982,581.57,3.01E-103,134.322,8759.03 +2,25.1355,114.005,0,1,-31.4356,0,114.005,0,-31.4356,0,1,25.1355,25.1355,36.5201,36.5201,36.5201,5791.19,0,429.178,11.1982,581.57,3.01E-103,134.322,8758.96 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+899,93.4529,134.519,7431.99,1,53.9725,7431.99,134.519,0,-31.4356,0,1,93.4529,93.4529,172.286,172.286,172.286,4932.97,0,719.732,8.67371,978.731,177.927,1550.96,8041.89 +899.5,93.5058,134.519,7430.56,1,53.9725,7430.56,134.519,0,-31.4356,0,1,93.5058,93.5058,172.286,172.286,172.286,4931.94,0,719.732,8.67371,978.731,177.927,1550.96,8041.89 +900,93.5058,134.519,7429.07,1,53.9725,7429.07,134.519,0,-31.4356,0,1,93.5058,93.5058,172.286,172.286,172.286,4930.91,0,719.732,8.67371,978.731,177.927,1550.96,8041.33 +900,93.5058,134.519,7429.07,1,53.9725,7429.07,134.519,0,-31.4356,0,1,93.5058,93.5058,172.286,172.286,172.286,4930.91,0,719.732,8.67371,978.731,177.927,1550.96,8041.33 From 19f426e4d12c218ada607ab543dd8636cf588b44 Mon Sep 17 00:00:00 2001 From: Anders Andreasen <58475535+andr1976@users.noreply.github.com> Date: Tue, 30 Dec 2025 17:06:39 +0100 Subject: [PATCH 5/6] Asdding rupture section in manual --- Manual.md | 59 +++++++++++++++++++++++++++++++++++++ docs/img/UTS.png | Bin 0 -> 380122 bytes docs/img/heat_capacity.png | Bin 0 -> 244727 bytes 3 files changed, 59 insertions(+) create mode 100644 docs/img/UTS.png create mode 100644 docs/img/heat_capacity.png diff --git a/Manual.md b/Manual.md index 05f7bb2..0abd03a 100644 --- a/Manual.md +++ b/Manual.md @@ -1000,6 +1000,65 @@ Both ASME F&D, DIN and 2:1 semielliptical are variants of a torispherical vessel Using the *fluids* library partial volumes, surface area (full and partial) and liquid level (from partial volume) can be calculated and used internally in *openthermo*. + +## Rupture evaluation +It is assumed that when the von Mises stress, $\sigma_e$ (MPa), exceeds the allowable tensile strength of the material, (ATS) (MPa), rupture will occur, i.e., when $\sigma_e$ > ATS. + +The ATS is calculated as [@scandpower]: + +$$ ATS = UTS k_s k_y $$ + +Where + +- $UTS$ is the material Ultimate Tensike Strength +- $k_s$ is a general safety factor for a specific material with known material data. If typical material specific data is applied a factor of 0.85 is recommended. +- $k_y$ is an additional factor used for material with missing or uncertain data. Normally this factor is 1.0. + +The von Mises stress is calculated by: + +$$ \sigma_e = \sqrt{3 \left(\frac{p D^2}{D^2 - d^2} \right)^2 +\sigma_a^2} $$ + +Where + +- $p$ is the pressure (MPa) +- $D$ is the vessel/pipe external diameter +- $d$ is the vessel/pipe internal diameter +- $\sigma_a$ is the longitudinal stress due to the external force. Assumed to be 30 MPa [@scandpower] + +The evaluation of vessel rupture is performed as a post-calculation step following the actual depressurisation calculation. The depressurisation calculation is performed with the applicable back-ground heat load to generate the time dependent pressure profile of the vessel inventory. The background heat load is depending on the fire type as also summarised in [@Tbl:heatfluxes1]. During the depressurisation calaculation the internal heat flux is calculated. In the post-calculation step an energy balance is made for the vessel material, with the external heat is generated by the applicable peak heat load Stefan-Boltzmann formulation as also provided in [@Tbl:heatfluxes1], with the internal heat flux calculated using the back-gorund heat load. The heat balance for the vessel wall is used to solve for the vessel wall temperature as a function of time + +$$ \frac{dT}{dt} = \frac{q_{external}-q_{internal}}{C_p \rho dx} $$ + +Where: + +- $T$ is the vessel wall temperature (K) +- $q_{external}$ is time dependent peak fire heat flux (W/m$^2$ K) +- $q_{internal}$ is the internal convective heat flux (W/m$^2$ K) +- $C_p$ is the material temeprature dependent heat capacity (J/kg K) +- $\rho$ is the materal density (assumed constant) (kg/m$^3$) +- $dx$ is the vessel wall material thickness (m) + +This oridinary differential equation is solved using a simple explicit Euler scheme. + +The temperature dependent material properties has been sourced from the Scandpower guideline [@scandpower] and visualised in [@Fig:heat_capacity] and [@Fig:UTS] for heat capacity and Ultimate Tensile Strength, respectively. The materials implemented in *openthermo* are summarised in [@Tbl:materials]. + +![Steel heat capacities as a finction of temperature for the materials implemented in *openthermo*. The values have been sourced from [@scandpower] and missing values extrapolated to cover the same temperature range.](docs/img/heat_capacity.png){#fig:heat_capacity} + + +![Steel Ultimate Tensile Strengt as a finction of temperature for the materials implemented in *openthermo*. The values have been sourced from [@scandpower] and missing values extrapolated to cover the same temperature range.](docs/img/UTS.png){#fig:UTS} + + +| Steel type | Type / alloy | ASME | DIN | ASTM | +|--------------|--------------|------|-----|------| +| Carbon steel | 235LT | | | A-333 / A-671 | +| | 360LT | | | | +| Duplex (SS) | 2205 | SA-770 | 1.4462 | A-790 | +| Austenitic (SS) | 316 | A-358 316 | 1.4401 | A-320 | +| Super austenitic (SS) | 6Mo | | 1.4529 | B-677 | + +: Steel materials implemented in *openthermo*. {#tbl:materials} + + ## Model implementation A simple (naive) explicit Euler scheme is implemented to integrate the mass balance over time, with the mass rate being calculated from an orifice/valve equation as described in [@Sec:flow]: diff --git a/docs/img/UTS.png b/docs/img/UTS.png new file mode 100644 index 0000000000000000000000000000000000000000..ce708d28275762581fd9196718fe2f95d8559493 GIT binary patch literal 380122 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import matplotlib.pyplot as plt from hyddown import HydDown - import scienceplots - plt.style.use(["science", "nature"]) + # import scienceplots + + # plt.style.use(["science", "nature"]) input = get_example_input("rupture.yml") hdown = HydDown(input)